Discourse, anaphora and parsing 
1. Introduction 
Mark Johnson 
Center for the Study of Language and Information 
and Dept. of Linguistics 
Stanford University 
Abstract 
Discourse Representation Theory, as formulated by Hans Kamp and others, provides a 
model of inter- and intra-sentential anaphoric dependencies in natural language. In this 
paper, we present a reformulation of the model which, unlike Kamp's, is specified deelara- 
lively. Moreover, it uses the same rule formalism for building both syntactic and semantic 
structures. The model has been implemented in an extension of PROLOG, and runs on a 
VAX 11/750 computer. 
The study of anaphora has been a central issue in both 
theoretical and computational linguistics. Studies of anaphora 
in theoretical linguistics usually concentrate on describing the 
constraints on sentence-internal anaphora (e.g. (Reinhart 
1983)). However, recent work by Hans Kamp (Kamp 1981) 
suggests that it is possible to describe some important aspects 
of inter-sentential anaphora while still respecting the con- 
straints of intra-sentential anaphora. In this paper we con- 
struct a model of anaphorie dependencies which is based on 
Kamp's theory of Discourse Representation (DRT), but 
expressed in the same declarative formalism that we use for 
describing syntactic structure. Unlike the standard DRT 
approach to constructing discourse representations, our model 
avoids any iaention of left-to-right processing. Note that we 
are not denying that there arc left-to-right dependencies in 
anaphora, nor are we denying that these dependencies ulti- 
mately arise from the fact that earlier parts of a discourse are 
processed before later parts of that discourse. Rather, we 
claim that such dependencies should not be stated implicitly in 
the specification of the processing strategy, but are better 
expressed as part of the formal description of the model. 
The idea of separating a computer program into two distinct 
parts: a logical specification of the problem to be solved, and 
a proof procedure that "interprets" this specification to actu- 
ally solve the problem has been a prominent idea in recent 
work on logle programming, especially in the work of Kowal- 
ski. We connect directly into this tradition, in that our specif- 
ication of DRS theory is provided in the form of an extended 
Horn-clause logic formalism. 
Our system thus consists of two parts: a logical specification 
of DRS theory, written in a language that we have dubbed 
PrAtt (for Prolog with Attributes), and a simple theorem 
prover (interpreter) which is capable of deducing the DRSs 
that correspond to various input sentences using the logical 
specification of DRS theory. 
In terms of Kowalski's (Kowalski 1979b) famous maxim 
"Algorithm = Logic + Control", the logical specification of 
the DRS theory corresponds to the "Logic", while the infer- 
ence technique used by the inference engine corresponds to 
the "Control". Currently our inference engine uses a simple 
top-down proof technique (inherited from Prolog, in which 
The research reported in this paper was conducted at 
the The (;enter for the Study of Language and Information, 
and was made possible in part by a gift from the System 
Development foundation, we gratefully acknowledge financial 
support from the National Science Foundation (grant BNS- 
8309780); and Klein also acknowledges financial support from 
the U.K. Science and Engineering Research Council (Ad- 
vanced FeUowship). Earlier versions of this paper were 
presented at at the Summer Meeting of the Association for 
Symbolic Logic, July 15-20 1985, Stanford University, and the 
Autumn Meeting of the Linguistics Association for Great Bri- 
tain, September 18-20 1985, University of Liverpool. 
We would like to express our appreciation for comments and 
suggestions from Jo Calder, Glyn Morrill, Carl Pollard, Fcr- 
nando Percira, John Perry, Ivan Sag, Stuart Shieber, and 
Henk Zeevat. 
Ewan Klein 
Centre for Cognitive Science 
\[formerly School of Epistemics\] 
Edinburgh University 
the inference engine is written), so the system as a whole (= 
logical specification of DRS theory + top-down theorem 
prover) functions essentially as a top-down predictive parser. 
However, this top-down behaviour is a property of the 
theorem prover only, and one could replace the theorem 
prover component with a more sophisticated proof technique 
such as Earley deduction (Pcreira and Warren 1983) resulting 
in a system that used a generalization of Earley's parsing 
algorithm. Such a change would be a change to the theorem- 
prover only, since both systems would use the same logical 
specification of DRT. 
2. A naive model of anaphorlc dependency 
In this section we give a brief overview of the basic ideas 
involved in the model. We do this by presenting a "naive" 
model provides the core of the analysis developed in section 
5, but which ignores the complexity of syntactic structure and 
quantifier binding. The naive model enables us to exolain our 
stance, independent of these complicating factors, on matters 
such as the changing natm'e of the discourse context over 
time, the mectlanisms used to describe reference, semantle 
gender agreement, etc. 
The following diagram (1) illustrates a naive declarative 
model of anaphoric dependency, where all that is required to 
license an anaphoric pronoun is the presence of a possible 
antecedent to its left. 
(1) { } {w} {w} {w,m} {w,m} {w,m} {w,m} 
Awoman kissed aman. He J touched her. \] 
In the naive model we conceive of a discourse context as sim- 
ply consisting of a set of individual names, or reference mark- 
ers. These represent the entities which are available to be 
talked about in the discourse, and play a similar role in our 
framework as the discourse entities of (Webber 1979). In 
particular, they provide tile set of possible antecedents for 
anaphorie noun phrases. We make the simplifying assump- 
tion that the only way for a reference marker to find its way 
into tile context is by courtesy of an indefinite description. 
We assume that reference markers are typed, and we adopt 
the convention of using 'f' as a marker for female gender enti- 
ties, 'm' for male gender entities, and 'x' for neuter or 
indeterminate gender entitie.s. 1 
The vertical bars in (I) represent moments of time in the 
analysis of the discourse; each moment is associated with a 
discourse context. In this way, we can characterize a develop- 
ing discourse context as a series of discrete states, each of 
which is localized at specific point in time and unchanging 
during the course of the parse. 2 In the diagram above, these 
I These three types of reference marker correspond to 
the genders available for pronominal agreement in English. 
However, it seems plausible that a more complicated account 
of agreement would be required for those languages (e.g. 
French and German) in which gender marking is semantically 
arbitrary. 
669 
contexts are shown above the bar that corresponds to the 
point of time at which they hold. Thus, at the beginning of 
the discourse the context was empty (i.e. the null set), while 
after the phrase a woman was uttered the context contained 
the single reference marker f. Consequently, { f } serves as 
the context for kissed. 
We view the meaning of a linguistic expression a as a relation 
between the context that preeeeds a and the context that fol- 
lows ~. That is, the meaning of ot has the general form 
shown in (2): 
(2) Preceding-Context \[ ~t \[ Following-Context 
Consequently, in the naive model the discourse context is 
determined by a series of equations relating the context which 
immediately precedes a lexical item to the context which 
immediately follows that item. For individual words, this 
relation is part of the lexical specification. To illustrate, the 
semantic contribution of woman is given here by (3a), or more 
generally, as (3b). 
(3a) {} I woman \[{f} 
(3b) C I woman I C U { f } 
The anaphoric pronoun her behaves in a very different 
fashion to indefinite noun phrases. Rather than adding a 
reference marker to the following context, it looks in the 
preceding context for a reference marker of the right sort (i.e. 
one that agrees with it in number and gender). If there is no 
such antecedent marker, the pronoun cannot be interpreted as 
anaphoric. The meaning of anaphoric her is the relation in 
(4). 
(4) ClherlCifff•C 
where f is the reference marker associated with her 
A sequence of discourse contexts is well-formed for a string if 
all of the relations associated with the lexieal items in the 
string hold; i.e. the discourse contexts arc a solution to the 
relational equations. Sometimes these equations wiil have a 
single solution; in that case, the discourse is unambiguous. 
However, usually the equations have multiple solutions, which 
means, in effect, that the discourse has many interpretations. 
This arises, in the present discussion, when a pronoun has 
several possible antecedents. 3 On the other hand, it is also 
possible that the equations have no solution at all. This case 
arises when a pronoun is used in a discourse context that con- 
tains no appropriate reference marker at all. 
At a more abstract level, we can view this model as one in 
which the context is a stream of reference markers, which is 
threaded from one lexical item to the next. The equations 
associated with individual iexical items act as (possibly non- 
deterministic) operators on their input stream to produce an 
output stream, which serves as the input to the following lexi- 
eel item. 
One of the main virtues of this simple picture is that it invites 
comparison with other ideas. Our proposed notion of mean- 
ing is clearly reminiscent of the claim in (Barwise and Perry 
1983) that meaning is a relation between different types of 
situation, though it also has its roots in earlier work on indexi- 
cal semantics, such as (Stalnaker 1972). Second, it is also 
2 It seems that this technique of factoring a single non- 
monotonic representation into a series of monotonic ones is 
applicable in many areas other than the one discussed here. 
At an abstract level it is similar to the technique discussed by 
(Kowalski 1979a). It is also similar to the use of difference 
lists in logic programming, since the "content" of a particular 
element is the difference bewteen its "output" and its "input". 
s In such a case, our program merely enumerates all pos- 
sible interpretations, which results in the familiar combinatori- 
al explosion of solutions. A better technique, which we can- 
not explore here, would be factor out the ambiguity and local- 
ize it in the representation. 
670 
reminiscent of the technique used in logic programming 
known as difference lists (Pereira 1985) or threading. 
3. Discourse Representation Theory 
The naive model presented in the last section ignored all syn- 
tactic and lexical interactions with the "left-to-right" nature of 
anaphoric dependency. The fatal flaw of this account is that 
is fails to explain the anaphoric propeties of universally quan- 
tified NPs. The data which shows this is well known, and 
some illustrative cases are given in (5) to (7). 
(5) a. A woman i went home. She. was tired 1 
b. Every woman i went home. She i was tired. 
(6) a. Every man i thought he i was ill. 
b. Lee gave every woman i her t prize. 
(7) a. Every man saw a woman t. She i was going home. 
b. Every woman who klssed a man I loved him 1. 
(5) shows that a universal NP does not normally act as an 
antecedent for pronouns in a following sentence. 4 According 
to the variable-binding paradigm of anaphora, this follows 
because a universal can only enter into an anaphorie relation 
with pronouns that are in its scope. For our current purposes, 
it is not important whether scope is determined in terms of a 
tree-geometrical notion like e-command (Reinhart 1983), or in 
terms of function-argument structure, as proposed by 
(Ladusaw 1980) and (Bach and Partee 1980); in either case, it 
is clear that the scope of the universal in (5) is that portion of 
the first sentence that we have italicised. Examples (6) illus- 
trate cases where a universal does enter into an anaphoric 
relation with a pronoun in its scope (again indicated by italiei- 
sation). (7) is intended to indicate the interaction between 
indefinites and universals. In (7a), the indefinite has narrower 
scope than the universal, and it is thereby incapable of acting 
as an antecedent for a pronoun such as the following she 
which is outsid the scope of the universal. By contrast, when 
both the indefinite and the pronoun fall within the scope of a 
universal, as in (7b), an anaphorie link is permissible. Note 
that (7b) is a so-called 'donkey' sentence. 
The study of these syntactic and lexieal effects has been a cen- 
tral theme of modern theoretical linguistics, but most work 
within this paradigm has concentrated almost exclusively on 
intra-sentential anaphora. However, recently (Kamp 1981), 
(Helm 1982) and (Haik 1984) have developed theories capable 
of providing a unified account of the main properties of intra- 
and inter-sentential anaphora. We will base our account on 
Kamp's Discourse Representation Theory, and in this section, 
we briefly outline those aspects of Kemp's model which are of 
most relevance to us. 
DRT is intended to explicitly capture the distinctions in ana- 
phoric potential exhibited by (ga) and (gb), while simultane- 
ously providing a basis for truth-conditional semantic interpre- 
tation. Thus (ga) would be associated with a DRS of the form 
(8). 
(g) f 
woman(f) 
went-home( f ) 
tired( f ) 
4 Sentences like (i) are exceptions to this generalization: 
(i) Every man will like this car. He'll certainly want to 
drive it. 
Rather than abandoning the generalization altogether, it 
seems more fruitful to adopt the hypothesis that such 
discourses involve 'modal subordination' (Roberts 1986) of 
the second sentence to the first. However, we do not under- 
stand the precise mechanics of this process. 
A discourse representation has two parts: a 'universe' consist- 
ing of set of discourse markers (in this case a singleton set) 
and set of conditions. The sentenee A woman went home 
licences the introduction of the reference marker f into the 
universe of the DRS, and this marker is also entered as the 
argument of tile predicate went-home. When She was tired is 
analyzed, the pronoun can be interpreted as anaphorie on a 
preceding NPs if the marker licensed by that NP is 'aecessio 
bit'; i.e. if tile marker belongs to the universe of the immedi- 
ately enclosing DR or a superordinate one. Since f is accessi- 
ble, the prouoan her can be identified with it to yield the con- 
dition tired(f). 
Before turning to sentences involving universal NPs, it will be 
useful to consider in a little more detail the procedure for con- 
structing a Dlt like (8) proposed by (Kamp 1981/. Karnp's 
rules pivot on the noun phrases in a sentence, and depend 
particularly on any determiners in the noun phrases. It is use° 
ful to think of every determiner as having a semantic restrictor 
and a semantic scope. The determiner will bind an argument 
position in each of these. Thus, in a simple intransitive sen- 
tence like tlu~ first sentence of (5), the restrictor of a is 
woman(), while its scope is went home(), where the empty 
parentheses indicate an open argument position. Given an 
existing (possibly empty) DRS K, a sentence of the form \[\[a 
Res\] Scope\] is "processed" in the following manner: 
(i) add a new reference marker x to the universe of K; 
(ii) fill the argument slot in Res by x, and add the resulting 
clause to the conditions of K; and 
(iii) fill the argument slot in Scope by x, and recursively call 
any applicable construction rules to process the resulting 
string. 
Let us turn now to sentences involving universals. The DR 
associated with (5b) is illustrated in (9). 
(9) 
f- 
\[ w°~mfan(f ) 1" l went-h°me(f~l 
tired( f" ) 
The universal quantifier every triggers the introduction of two 
subordinate DRSs, linked by the relation =>; this 
corresponds roughly to implication in first order logic. When 
we come to analyze the second sentence of the discourse, She 
was tired the reference marker licensed by every woman is 
trapped in the subordinate DRS; it is not accessible at the top 
level of the discourse. Consequently, the only option is to 
treat the pronoun she as non-anaphorie, which we have indi- 
cated here by associating it with a distinct reference marker. 
When we consider sentence-internal anapbora, the 
antecedent-introducing potential of every and a converge. For 
example, in both of the following sentences, he can be ana- 
phoric to the subject NP: 
(6a) t?,very man i thought he i was ill. 
(10) A man i thought he i was ill. 
Although it may not be obvious from the examples given so 
far, DR theory correctly predicts that the reference markers 
associated with an indefinite or universal NP in subject posi- 
tion will be anaphorically accessible to pronouns that it c- 
commands. 5 To see why, we need to consider in a little more 
5 It might be argued that DR theory fails to provide an 
adequate semantic distinction between a 'c-command binding' 
relation and a 'discourse anaphora' relation, as proposed for 
example by (Rcinhart 1983) in order to account for the 
strict/sloppy ambiguity in VP ellipsis. Whether this criticism 
is justified or not depends in large part on the appropriate 
analysis of such ellipsis phenomena in the DR framework. 
For some discussion, see (van Eijck 1985), (Klein 1985), 
(Roberts 1984). 
detail tile way in which DR's are coustructcd on g~amp's 
approach. 
Construction rules apply to sentences on a top-down, left-too 
right basis. Given a sentence like (6a) or (10), the first con- 
stituent to be processed is tile subject NP. We either stay in 
the current DR, if tile determiner is a, or 'push down' to an 
embedded DR if the determiner is every. (This embedded 
DR is, therefore, the antecedent box of tile conditional like 
that displayed in (9).) A discourse marker x i is introduced 
into the universe of whatever is now the current DR, and x i 
also becomes the argument of the subject nominal (e.g. 
man(rot)) and the first argument of the predicate VP (e.g. m t 
thought he was ill). When tile VP is processed, there are 
again two cases, depending on whether tile subject determiner 
was a or every. In tile first ,:;ase, we enter tile new conditions 
licensed by the VP into the current DR. Ill the second case, 
we close off the current (antecedent) DR, and open a new 
embedded DR which forms the conseqent box of the condi- 
tional. Kamp claims that the reference markers accessible as 
antecedents to a given pronoun occurrence consist of those 
reference markers which are present in the universe of either 
the current DR or of any DR.'s which are superordinate to the 
current DR. Of two DR's K 1 and K2, K 1 is superordinate to 
I{ 2 if: 
(i) K 2 is embedded in K1, or 
(ii) if K 1 is the anteeedeut of a conditional of which K 2 is 
tile consequent, or 
(iii) if there is some K~ such that K 1 is superordiaate to K 3 
and K 3 is I;uperordmate to K 2. 
This is illustrated in (11) diagram below, where tile lightly 
shaded boxes arc all superordinate to the darkly shaded box. 
(II) ============================================================================== 
I 
Consider now what follows when we come to process the NP 
he in either (6a) or (10). It can be anaphorically linked to any 
reference marker which is accessible to it, and this will of 
course include the marker x i introduced by the subject NP. 
Let us now attempt to summarise the salient features of DRT. 
Note, first, that every noun phrase is associated with a 
'space '6 in a Discourse Representation. Referential terms - 
which we take to include definite and indefinite descriptions, 
proper names, and definite pronouns - are entered into an 
existing space. By contrast, universally quantified NPs induce 
a new subspace~ 
Second, the space associated with an NP represents both the 
quantificational scope of the NP and its anaphoric domain. 
Third, the boundaries of these spaces are not coterminous 
with clause or sentence boundaries. A clause containing 
universal NPs will induce a number of subspaces; conversely, 
the space associated with a referential NP can encompass 
indefinitely many sentences of a given discourse. 
Fourth, the space of an indefinite NP which occurs within the 
scope of a uniw~rsal NP is the same as the space of the univer- 
sal. 
4. The flow of anaphorlc Information 
In the last section we showed how DRT is able to simultane- 
ously describe both the semantics of quantification and tile 
anaphorie 'range' of referential noun phrases in terms of a 
single discourse representatkm. The standard version of DRT 
depends crucially on processing notions in order to explain the 
failure of anaphora in examples like (12). 
671 
(12) He i liked a boy i. 
Since the reference marker for a boy is not introduced into the 
DR until after the pronoun he is introduced, it is unavailable 
as a possible antecedent. That is, the failure of anaphora is 
explained by assuming that the pronoun's antecedent is 
assigned at the time at which it is introduced into the DRS, 
and that the reference marker for the noun phrase is intro- 
duced after the pronoun was introduced. 
In a declarative framework, an explanation in terms of pro- 
cessing order is impermissible hence we represent left-to-right 
dependencies by explicit equations. Although these equations 
are in principle non-directional, it can be helpful to think of 
them as providing a means for transmitting information from 
one node in the syntactic structure to another. 
Bottom-up information flow is central to syntax-drlven com- 
positional semantles of the familiar sort: semantic values are 
associated with the leaves of the syntax tree, and the semantic 
value of a complex constituent is determined as a function of 
the semantic values of the constituents daughters. The 
diagram in (13) shows this direction of information flow. 
(13) S kissed'( a'(boy9 )(a'(girl') ) 
NP a'(girl') VP kissed'(a'(boy') ) 
Det a" N girl" V kissed" NP a'(boy') ) 
i !, Jsed a gi Det a" N boy" 
Although this approach has proven to be extremely powerful, 
it is awkward and intuitively unsatisfactory as a means for 
dealing with anaphorie dependencies. Even if much semantic 
information is indeed composed on a bottom-up regime, it 
seems highly plausible that anaphorie information - that is, 
information about the set of available antecedents - flows in 
a left-to-right direction. We have already seen that a simple 
left-to-rlght model of this information flow can be constructed 
by regarding meaning as a relation between contexts, but we 
have also seen that such a model is inadequate for dealing 
with the facts of bound anaphora. A more satisfactory model 
can be constructed by reflecting on the principles involved in 
constructing Discourse Representations. As we pointed out in 
the previous section, Kamp's construction rules centre on the 
determiners a and every, since they trigger the introduction of 
reference markers, the binding of argument positions, and the 
introduction of sub-spaces. What we shall suggest, therefore, 
is that information about possible antecedents flows from a 
determiner to the determiner's restrietor, and from the restrie- 
tot to the determiner's scope. The following diagram (14) 
illustrates how this top-down, left-to-right flow is integrated 
with the orthodox phrase marker of a girl kissed a boy. 
(14) {L {b,g} 
I I I a g'~\[l '~x ki!sed L~ {b,g} 
a I 
s This term is intended to be reminiscent of work by Fau- 
connier (1985) on mental spaces, and by Reichman-Adar 
(1984) on context spaces, though considerable work needs to 
be done in showing that these ideas are in fact compatible. 
672 
The light, incoming lines on the left-hand side of a node indi- 
cate incoming information about the set of possible 
antecedents. This set will be encoded in something we call the 
"in-list". The light lines on the right-hand side of a node indi- 
cate outgoing ~ information about antecedents, encoded in the 
form of an "out-list". In general, the out-list of any node will 
be its in-list plus any additional information added by that 
node. Circled nodes mark constituents that supplement their 
in-list with new reference markers. The in-list and the out-list 
together form a difference list, in that the content added by 
any item is the difference between its in-list and out-list. 
Alternatively, one can view the in-lists and the out-lists of 
nodes as streams along which information about antecedents 
flows: this anaphoric information is threaded through the syn- 
tactic tree structure. Notice that we assume the sentence as a 
whole will be fed an in-list which is supplied by the preceding 
discourse. Moreover, the sentence as a whole will also a pro- 
duce an out-list, which will provide potential antecedents for 
following discourse. 
The next diagram (15) illustrates the flow of information for 
every girl kissed a boy. 
1 ~, {} {} 
:very git~ kissed -~_.£d. J""~ ~K~) {b,g} 
! J 
By contrast with (14), the out-list from the VP, containing 
reference markers for gtrl and boy, is "trapped" at that level 
rather than percolating up to the S node. The out-list for the 
sentence as a whole is just the sentence's in-list. This captures 
the idea from binding theory that the scope of a quantifier is 
normally limited to its e-command domain (Reinhart 
1981, Reinhart 1983); In terms of DRT, it corresponds to the 
closed subspace that is associated with universal NPs. 
Let us summarize our claims so far. We have suggested that 
there is a contrast between the bottom-up information flow of 
compositional semantics, on the one hand, and the top-down 
flow that is naturally associated with anaphoric information. 
We have also suggested that top-down flow is largely deter- 
mined, according to the principles of DRT, by the lexical pro- 
perties of determiners and their structural position in the sen- 
tence. 
One possible implementation of this analysis would be to fac- 
tor out anaphoric, contextual information from the rest of 
semantics, and to use two distinct mechanisms for building the 
two kinds of representation. However, such an approach fails 
to explain why the spaces in a DR, and the list of 
contextually-divan antecedents always covary; that is, when a 
new DR subspace is opened, a new context list begins, and 
when a DR subspace is closed, a context list is simply 
"dropped", ie. it does not serve as the in-list to any other 
expression. Indeed, the fact that a DRS in Kamp's theory 
consists of a universe, corresponding to our context list, and a 
set of conditions, corresponding roughly to compositional 
semantic information, suggests that it out to be possible to 
enrich the notion of a context from being just a list of 
antecedents to being a whole DR structure. 
In our analysis, then, we thread a list through the syntactic 
structure which contains both conventional semantic informa- 
tion and information about available antecedents, so that an 
expression mapping an incoming context into an outgoing con- 
text does more than incrementing the set of possible 
antecedents: it also adds conditions to the context that 
correspond to its truth-conditional semantics. 
It is necessary that the context be structured, rather than a 
simple list, as it was in the naive model, and as discussed 
above. This is because we need to be able to incorporate the 
semantic structures associated with all expressions, even those 
that are anaphorically opaque to following anaphora. In the 
model described immediately above, we accounted for the 
anaphoric opacity of an expression by "dropping" its context 
list after it had been processed, but such "dropping" in a sys- 
tem where the context lists also contain "compositional" 
semantic information would result in that semantic informa- 
tion also being lost. 
Rather, we structure the context list as an ordered list of the 
currently open DR spaces, starting at the most embedded 
space, and working upward through the superordinate spaces. 
For example, the context list for an item located in DR space 
K 1 in (11) would be \[ K., K~, K~, K-\], where each K. is a 1 z 4 1 
set of reference markers and eon~tions, the current contents 
of the corresponding space. The first space on the context list 
is the most embedded space, ie. the current space, and identi- 
ties the place where new conditions and reference markers are 
to be added. Since the context list consists of the active space 
plus all of the spaces snperordinate to it, any reference mark- 
ers contained in these spaces are possible antecedents for ana- 
phora in the active space. 
5. The Grammar 
We turn now to considering the induction of DRSs. In this 
section we describe a simplified version of ttle grammar that 
we have implemented. The grammar presented here is the 
actual input to the proof procedure: the parser is nothing 
more than a declarative statement of the well-formedness con- 
ditions of an utterance, plus a proof procedure capable of 
determining whether or not these conditions actually hold of a 
given utterance. 
The rules are written in DCG format (Clocksin and Mellish 
1984) in a superset of Prolog that we developed in this pro- 
ject. This language, which we have dubbed PrAtt (for Prolog 
with Attributes), allows an attribute-value notation as well as 
the standard position-value notation of Prolog. For example, 
the expression "N:syn:index" refers to the value of the Index 
attribute of the syn attribute of the variable N. 
We make heavy use of the attribute-value notation to 
represent feature bundles associated with constituents. Two 
attributes that are present on every constituent are syn (for 
"syntax") and sam (for "semantics"). The sam:in and sam:out 
attributes contain the context in-lists and out-lists respectively, 
while the syn attribute holds information used to construct the 
function-argument structure of the clause. 
Expressions act on the context list by opening or closing 
spaces (ie. pushing or poping spaces from the context list), 
adding reference markers and conditions to the active space, 
and looking through all of the spaces in the context list for 
antecedents for anaphora. 
Consider, for example, the common noun woman. It inserts a 
reference marker f and a condition woman(f) into the active 
space. Using our earlier relational notation, we can express 
its meaning as follows: 7 
(16) \[ActiveJSuper\] I woman I \[if, woman(f) ~Active\]~uper\] 
In our implementation, this would be written as in (17). 
(17) n(N)--> \[woman\], 
{ N:syn:index = w, 
N:sem:in = \[ Current I Super \], 
N:sem:out = \[ \[ w, woman(w) \[ Current \] I Super \] }. 
7 We use standard Proiog notation here: variables begin 
with a capital letter, constants with a lower-case letter, "ix,y\]" 
is the list that contains x and y, and "\[x~\]" is the list that con- 
sists of x CONScd onto y. 
Tile hracketted equations are conditions that must be satisfied 
in rewriting an N to the lcxical item woman. The first equa- 
tion assigns a reference marker to the lexieal item, s the 
second equation analyses the incoming context list into two 
parts, the current space (Current) and a list of the superordi- 
nate spaces (Super), while the third equation requires the 
active space of the outgoing context list to contain the refer- 
enco marker and the condition associated with the noun. 
A sample entry for a verb is shown in (18). Again, the equa- 
tions associated with the lexieal entry dissect the incoming 
context into the current space and a list of superordinate 
spaces, and place the condition associated with the verb into 
the outgoing context. 
(18) 
v(V)--> \[saw\], 
{ V:sem:in = \[ Current I Super \] , 
V:sem:out = 
\[ \[ saw(V:syn:argl, V:syn:arg2) I Current \] I Super \] }. 
One interesting property of this rule is that it is responsible 
for placing a condition into the context that in essence 
represents the compositional semantics of the entire clause. 
The ~yn attributes of constituents are used to councct the NP 
arguments of the verb with the verb itself; thus the necessary 
information to build tile condition associated with the entire 
clause is available at the verb. One can view the equations in 
the phrase structure rules associated with the syn attribute as 
directing information from the NP arguments inward and 
downward to the verb. 
The crux of the grammar is located in the lexical entries for 
determiners, as hinted earlier. (19) contains tim lexical entry 
for the indefinite artlele a. 
(19) det(Det)..-> \[a\], 
{ Det:sem:res:in = Det:sem:in, 
Det:sem:scope:in = Det:sem:res:out, 
Det:sem:out = Det:sem:scope:out }. 
As we shall see later, the phrase structure rules are written in 
such a way that the value of the elauses's sam attribute is 
equal to its subject's determiner's sam attribute, and the 
semantics attribute of the restrictor and the scope of a clause 
are placed in that determiner's sem:res and sam:scope attri. 
butes respectively. As noted earlier, an indefinite determiner 
does not cause the creation of any additional subspaces, rather 
the restrietor and the scope are simply placed into the current 
active space. Therefore, the equations associated with the 
indefinite determiner simply connect the in-list asssociated 
with the sentence to the restrictor's in-list, feed the restrietor's 
out-list to the scope's in-list, and take the out-list from the 
scope as the out-list for the clause as a whole. 
The lexical entry associated with the universal quantifier every 
is a little more complicated. It must create two new spaces, 
one for the restrictor, the other for the scope, and the finally 
close off both spaces, and huild the structure associated with 
the clause as a whole. 
(20) det(Det)--> \[every\], 
{ Det:sem:res:in = 
\[ \[\] \] Det:sem:in \], 
Det:sem:scope:in = 
\[ \[\] I Det:sem:res:out \], 
Det:sem:seope:out = 
\[ Scope, Res I \[ Current \[ Super \] \], 
Det:sem:out = 
\[ \[ ( Res ==> Scope) ICurrent \] \]Super \] }. 
S For simplicity here we have reference markers directly 
to lexieal entries; however more correctly the reference mark- 
ers should be assigned to lexieal tokens, allowing two occu- 
rances of the same lexical entry to refer to different objects in the world. 
673 
The first equation in (20) pushes a new, empty space onto the 
determiner's in-list as the active space, and makes that list the 
restrictor's in-list. The second equation takes the restrictor's 
out-list pushes another new, empty space onto it, and makes 
the resulting list the scope's in-llst. The final equation takes 
the scope's out-list, removes the two spaces that were added 
for the restrietor and the scope, and produces a new list in 
which the original active space has a complex condition added 
to it representing the whole universally quantified expression. 
This last list serves as the outqist for the determiner, and 
hence for the clause as a whole. 
Below are the phrase structure rules responsible for connect- 
ing the various attributes of the constituents as described 
above. 
(21) np(NP) --> { NP:sem = Det:sem, 
Det:sem:res = N:sem, 
NP:syn = N:syn }, 
det(Det), n(N). 
(22) vp(VP) --> { VP:sem = NP:sem, 
NP:sem:scope = V:sem, 
VP:syn:arg2 = NP:syn:index, 
VP:syn = V:syn 
}, 
v(V), np(NP). 
(23) s(S) --> { S:sem = NP:sem, 
S:syn = VP:syn, 
NP:sem:seope = VP:sem, 
VP:syn:argl = NP:syn:index 
}, 
np(NP), vp(VP). 
It remains only to give the lexical entry associated with pro- 
nouns, and our fragment is complete. This is given in (24). 
(24) np(NP)--> \[her\], 
{ member(Space, NP:sem:in), 
member(NP:syn:index, Space), 
type(NP:syn:index,feminine), 
NP:sem:scope:in = NP:sem:in, 
NP:sem:out = NP:sem:scope:ont }. 
The first three equations require that there be some space 
containing a reference marker of feminine type with which the 
pronoun's reference marker can unify: 9 the last two equations 
take account of the fact that an anaphoric pronoun, while not 
adding any conditions of its own to the context, can appear in 
subject position, and thus can have a scope expression. 
We have now completely described our declarative formula- 
tion of DRS theory. This formulation (together with phrase 
structure rules that analyse a discourse as a series of sen- 
tences) suffices to obtain the analyses shown below) ° 
(25) Every woman chased a donkey. 
DRS = \[\[w,woman(w)\]= =>\[chased(w,d), 
d,donkey(d)\]\] 
(26) A woman chased a donkey. Every boy saw her. 
DRS = lib,boy(b)\]= =>\[saw(h,w)\], 
\[d,donkey(d)\] = = > \[ehased(w ,d)\], 
w,woman(w)l 
9 The definition of member used here is the conventional 
one used in Prolog (albeit interpreted by the PrAtt inter- 
preter, while the type predicate is a set of clauses of the form 
type(w,feminlne)., etc. 
l0 Note that because later elements are pushed onto the 
front of a DR space, the order of the elements in the DR 
spaces is the reverse of their "normal" pr.~'~entation. This 
does not affect their truth conditional semantics, however. 
674 
We have also implemented a more complex version of this 
grammar incorporating a treatment of unbounded dependen- 
cies, and obtained analyses like the following: 
(27) Every man who owns a donkey beats it. 
DRS = \[\[man(m),owns(m,d),d,donkey(d),m\] 
= = > \[beats(re,d)\]\] 
Tile parser indicates ill-formedness of its input in the standard 
Prolog fashion, viz. it fails to find a well-formed DRS for the 
input sentence. 
(28) A woman who loves every man kissed him. 
no 
6. Conclusion 
The declarative reformulation of DRS theory proposed here is 
relatively faithful to Kamp's original formulation, but has the 
advantage that it inherits a fully specified declarative and pro- 
cednral semantics from the underlying Prolog system. It 
emphasises tlle view that expressions of the language can be 
viewed as relations between preceding and following contexts, 
and shows how these relations can be specified in a formally 
precise way. 
This model opens up several important questions. Kamp 
showed that the treatment of anaphorie dependencies, nor- 
mally viewed as a left to right phenomenon, can be integrated 
with the treatment of the "conventional" truth-conditional 
semantics of clauses: we have shown that both of these can be 
integrated into an extended unification-based model of gram- 
mar. This integration allows one to be precise about the 
nature of the syntax/semantics/discourse interface(s), and also 
allows experimentation with respect to the analysis of specific 
linguistic phenomena. For example, in our larger grammar 
(not presented here) we capture strong and weak cross-over 
phenomena by introducing the reference marker associated 
with a relative clause NP when the corresponding gap is 
reached. We are thus analysing what is usually thought of as 
a syntactic phenomenon in terms of the accessibility of refer- 
ence markers, a discourse property. 
From a computational point of view, there is a delicate 
interaction between the specific rules adopted in declarative 
formulation of the theory and the "power" of the inference 
procedure needed to determine the well-formedness of a par- 
titular utterance with respect to them. The top-down left-to- 
right inference procedure inherited from Prolog suffices for 
the grammar presented here, but one can easily write gram- 
mars in PrAtt for which this inference procedure may fail to 
terminate. We are investigating other inference procedures, 
such as Earley Deduction (Pereira and Warren 1983) and Left 
Corner parsing to see if they have better termination proper- 
ties. Essentially, the problem is one of arranging the equa- 
tions in the grammar to be applied in an order such that the 
search space is finite: thus research on various coroutining 
strategies, such as the use of the freeze predicate is relevant 
here. 

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